91Ó°ÊÓ

The radius of the earth’s orbit around the sun (assumed to be circular) is 1.5x10⁸ km, and the earth travels around this orbit in 365 days. (a) What is the magnitude of the orbital velocity of the earth, in m/s? (b) What is the radial acceleration of the earth toward the sun, in m/s? (c) Repeat parts (a) and (b) for the motion of the planet Mercury (orbit radius is 5.79x10⁷ km, the orbital period is 88.0 days.

A slab of ice floats on a freshwater lake. What minimum volume must the slab have for a 65.0-kg woman to be able to stand on it without getting her feet wet?

28)Four small spheres, each of which you can regard as a point of mass of 0.200 kg, are arranged in a square of 0.400 m on a side and connected by extremely light rods (Fig. E9.28). Find the moment of inertia of the system about an axis

(a) through the center of the square, perpendicular to its plane (an axis through point O in the figure);

(b) bisecting two opposite sides of the square (an axis along the line AB in the figure);

(c) that passes through the centers of the upper left and lower right spheres and point O.

A car sits on an entrance ramp to a freeway, waiting for a break in the traffic. Then the driver accelerates with constant acceleration along the ramp and onto the freeway. The car starts from rest, moves in a straight line, and has a speed of 20 m/s (45 mi/) when it reaches the end of the 120-mlong ramp. (a) What is the acceleration of the car? (b) How much time does it take the car to travel the length of the ramp? (c) The traffic on the freeway is moving at a constant speed of 20 m/s. What distance does the traffic travel while the car is moving the length of the ramp?

A fellow student with a mathematical bent tells you that the wave function of a traveling wave on a thin rope is\(y\left( {x,t} \right) = 2.30\,mm\,cos\left[ {\left( {6.98\,{{rad} \mathord{\left/{\vphantom {{rad} m}} \right.

\nulldelimiterspace} m}} \right)x + \left( {742\,{{rad} \mathord{\left/{\vphantom {{rad} s}} \right.

\nulldelimiterspace} s}} \right)t} \right]\). Being more practical, you measure the rope to have a length of \(1.35 m\) and a mass of\(0.00338 kg\). You are then asked to determine the following: (a) amplitude; (b) frequency; (c) wavelength; (d) wave speed; (e) direction the wave is traveling; (f) tension in the rope; (g) average power transmitted by the wave.

A soccer ball with mass 0.420 kg is initially moving with speed 2 m/s. A soccer player kicks the ball, exerting a constant force of magnitude 40.0 N in the same direction as the ball’s motion. Over what distance must the player’s foot be in contact with the ball to increase the ball’s speed to 6.00 m/s

You are standing on a large sheet of frictionless ice and holding a large rock. In order to get off the ice, you throw the rock so it has velocity 12.0 m/s relative to the earth at an angle of 35.0 degree above the horizontal. If your mass is 70.0 kg and the rock’s mass is 3.00 kg, what is your speed after you throw the rock?

A box of bananas weighing 40.0 N rests on a horizontal surface. The coefficient of static friction between the box and the surface is 0.40 , and the coefficient of kinetic friction is 0.20 . (a) If no horizontal force is applied to the box and the box is at rest, how large is the friction force exerted on it? (b) What is the magnitude of the friction force if a monkey applies a horizontal force of 6.0 N to the box and the box is initially at rest? (c) What minimum horizontal force must the monkey apply to start the box in motion? (d) What minimum horizontal force must the monkey apply to keep the box moving at constant velocity once it has been started? (e) If the monkey applies a horizontal force of 18.0 N , what is the magnitude of the friction force and what is the box’s acceleration?

In March 2006, two small satellites were discovered orbiting Pluto, one at a distance of 48,000 km and the other at 64,000 km. Pluto already was known to have a large satellite Charon, orbiting at 19,600 km with an orbital period of 6.39 days. Assuming that the satellites do not affect each other, find the orbital periods of the two small satellites withoutusing the mass of Pluto.

A nylon rope used by mountaineers elongates 1.10 m under the weight of a 65.0-kg climber. If the rope is 45.0 m in length and 7.0 mm in diameter, what is Young’s modulus for nylon?